M933157 Mersenne number exponent details

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M933157

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is 2 ⁹³³¹⁵⁷ - 1

has 280909 decimal digits

takes 0.023 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	52E71CE1058DD7__	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	31.8424	70.1493%	1000000	30000000	0.0907	5.7411%	31.9331	71.8630%	1.7138%
PrimeNet	2⁴⁰	0.0000	50.0000%	8000	360000	0.0010	23.4057%	0.0010	61.7028%	11.7028%
GPU72	2⁴⁴	0.0000	54.5455%	15000	600000	0.0016	18.0571%	0.0017	62.7532%	8.2078%
Difference	+23	+31.8424	+15.6038%	+985000	+29400000	+0.0891	-12.3160%	+31.9314	+9.1098%	+9.1098%

Known prime factors (1 factor, 67.7 bits, 0.00724996% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
933157	232127594865515676991	21	67.653	124377567154035 3 × 5 × 13 × 23 × 27731899031	2007-09-10	23	27731899031	33.194	53.127	99.227

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-08T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.213%
2002-02-24T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.452%
2002-04-28T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.811%
2002-05-25T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.004	-	-	1.313%
2002-07-27T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.007	-	-	1.962%
2002-12-31T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.015	-	-	2.752%
2003-09-09T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.029	-	-	3.669%
2016-03-17T18:54:29	alpertron	Manual testing	200000	5000000	6	-		-	-	0.016	-	-	3.280%
unknown			1000000	30000000		-		-	-	0.091	-	-	5.741%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-06-28T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.005	-	-
2000-06-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.005	-	-
2000-12-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.010	-	-
2001-10-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.021	-	-
2003-08-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.041	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.131 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	14.131 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
		232127594865515676991	1	0.00000e+0
50000	5000000		281	7.926
250000	25000000		44	6.205

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-10T19:14:00	Chad Davis	Bayes			232127594865515676991	67.653		1		1	-
2016-03-24T20:26:23	TJAOI	Manual testing	50000	5000000						100	2.821
2017-01-13T18:11:50	TJAOI	Manual testing	50000	5000000						90	2.539
2017-08-04T10:35:46	TJAOI	Manual testing	50000	5000000						91	2.567
2019-11-25T15:11:32	TJAOI	Manual testing	250000	25000000						44	6.205

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2001-12-01T00:00:00	ANONYMOUS	v4_computers	52E71CE1058DD7__	0.023

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T10:24:33

Oliver Kruse

GTX-3

232127594865515676991

D677B57DFC2886__

2017-10-14T23:20:58

Oliver Kruse

Threadripper

D677B57DFC2886__

2017-12-22T17:31:06

ATH

ec2-1xf

232127594865515676991

D677B57DFC2886__

2020-04-23T18:34:00

Oliver Kruse

AddPrpType5

232127594865515676991

88A5FE634143D4__

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 200000, B2 = 5000000 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 65536 (P-1 stage 1)

B1 = 8192, B2 = 819200 (P-1 stage 2)

B1 = 32768 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 200000 (P-1 stage 2)

B1 = 8192 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-04-23T18:34:00+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront